Ref 330.

The 238U, 235U, 232Th, 187Re, 176Lu, 147Sm, 87Rb, and 40K half-lives used by physicists, geochronologists, chemists; a review of their funding data. Bull. Liais. Inform. Subcommission on Geochronology, 15 : 31-41.

G. S. Odin, G. Audi & M-M. Bé, 1999.

GA: C.S.N.S.M. (IN2P3-CNRS) Bât. 108; 91405 Orsay Campus (France) phone +33 1.6915.5223 fax… 5268; adrel/email: amdc.audi@gmail.com; web http://www-csnsm.in2p3.fr/amdc
MMB: CEA DAMRI, Laboratoire Primaire des Rayonnements Ionisants, BP 52, 91193 Gif-sur-Yvette cedex; couriel: mmbe@cea.fr


Résumé : Divers écrits récents ont suggéré qu'il était temps de faire une révision des valeurs de constantes de désintégration et de composition isotopique utilisées depuis les recommendations de la sous commission de géochronologie 1977. Avec la coopération d'experts physiciens, chimistes et géochronologistes, le point des information utilisées par ces 3 communautés a été fait et est présenté ici. Les faits analytiques utilisés par les 3 communautés sont les mêmes pour l'uranium et datent de 1971; il en est pratiquement de même pour le thorium, le rubidium, et le potassium. Pour le 87Rb, la seule étude nouvelle date de 1977 et confirme la valeur adoptée par les géochrologistes la même année; une comparaison géochronologique U-Pb / Rb-Sr publiée en 1982 est aussi compatible et devrait être considéré pour le calcul d'une constante "améliorée". Pour le potassium, les différentes constantes utilisées par les 3 communautés ne sont que des calculs différents sur les mêmes valeurs publiées, pour l'essentiel, avant 1967. Aucun progrès n'est décelable depuis 20 voire 30 années dans la connaissance de ces isotopes.
Pour le 147Sm, l'usage des géochronologistes initié en 1982 (106,0 Ga) est toujours conforme aux recommendations récentes des physiciens et chimistes basées sur les mêmes résultats. Pour le 187Re, une recommendation pour une demie vie de 42.3 Ga (d'après la plus récente étude datant de 1989) pourrait être faite. Pour le 176Lu, les données actuelles de la littérature montrent une incohérence significative avec, à la fois, des valeurs voisines de 36 à 38 Ga et des valeurs voisines de 40-41 Ga; une valeur incertaine de 37.5 Ga pourrait être suggérée.
Un protocole expérimental destiné à améliorer cette situation est à l'étude et des moyens sont recherchés pour sa mise en oeuvre.

1. Introduction

Since 1977, geochronologists use the decay constants recommended by the Subcommission on Geochronology (SOG). The unstable isotopes 238U, 235U, 232 Th, 87Rb, and 40K were considered by Steiger & Jäger (SJ, 77). No values were recommended for the 187Re, 176Lu, 147Sm isotopes at that time. For the latter, an additional convention has been proposed in 1982 (Gale in Odin, 82; ref. 100). Finally, Renne et al. (1998) considered the values by Tatsumoto et al., 1981 (176 Lu) and Lindner et al., 1989 (187Re) as their preferred ones for geochronology.
The physicists community uses the decay properties gathered in the Nuclear Data Sheets edited by the Brookhaven National Laboratory. These properties have been evaluated by a committee of experts and the resulting information can be consulted in the Evaluated Nuclear Structure Data Files (ENSDF). The latter data and the Atomic Mass Evaluation of 1995 have been considered together with additional information absent from the 2 former evaluations to derive the database: NUBASE which is a critical compilation of the published data (Audi et al., 1997).
The International Union for Pure and Applied Chemistry (IUPAC) published recommendations for total half lives for selected nuclides (Holden, 1989, 1990). In addition, the same organisation publishes (and revises) the "Isotopic compositions of the elements". The last version considered here is that dated 1991 (IUPAC, Pure & Appl. Chem. 63: 991-1002.)
Recent discussions within the geochronological community suggest that the significant technical progress in analytical precision obtained during the last 20 years cannot benefit to the geological knowledge
1- because the 1977 recommended disintegration constants are not known with a precision similar to the analytical one and
2- because there is a distinct difference between the recommended values used by different communities especially the physicists (understated: who know decay constants better than in 1977).

This report results from an evaluation of the experimental sources considered by the different communities with the aim at identifying the progress (actual or not) which has been done since 1977. The final aim is to suggest potential changes of values able to allow more accurate geochronological ages to be calculated in a near future.
This review is also aimed at identifying what could be the best possibilities for improving further the knowledge of the physical basis.

2. Comparison of data for usual geochronological systems

238U

-"Physicists' value"
The data in ENSDF are as follows:
............238U......L 0.0....... 0+.................4.468e+9 y ±3
............4.49e+9 y ±1..............(49Ki26),......PHRVA 76 1561
............4.507e+9 y ±9............(55Ko13),......HRVA 98 46
............4.51e+9 y....................(57Cl16),......JSACA 10 62
............4.56e+9 y ±3..............(57Le21),......JNCEA 4 38
............4.46e+9 y ±1..............(59St45),......CONF Vienna (Metrology Radionucl.) p.155
............4.4683e+9 y ±24........(71Ja07).......PRVCA C4 1889

The preferred value for physicists (4.468 ±3 Ga) is simply the rounded value by Jaffey et al., 1971 (4.4683 ±24). The original more precise value might appear preferable for geochronologists.

-"Geochronologists' value"
............SJ 1977 favoured the original data by Jaffey et al., 1971 (71Ja07): 4.4683 Ga ±24.

-"Chemists' value"
............The value recommended by Holden (1989) is given as 4.47 ±0.02 Ga and is said to be selected from Jaffey et al.; but the value reported for Jaffey et al. is given by Holden as 4.468 ±22 with an uncertainty mistakenly multiplied by 10.

235 U

-"Physicists' value"
The data in ENSDF are as follows:
............235U......L 0............7/2-............703.8e+6 y 5............ 930831
T from 71Ja07 (PRVCA C4 1889);
Others : 71Ar48 (NDSBA B6 287), 74De19 (PRVCA C10 383), 74Ja17 (PRVCA C10 386). The systematic uncertainty dT is estimated by 71Ja07 to be no larger than twice the quoted statistical dT.

-"Geochronologists' value"
............SJ 1977 favoured the original data by Jaffey et al., 1971 at 0.70381 (±48) Ga.

-"Chemists' value"
............Holden (1989) quotes 9 values from the literature and calculate a weighted average which is given as 0.704 ±0.001 Ga and recommended. In this calculation the Jaffey et al. value (incorrectly reported as 0.7037 ±0.0011) which has an analytical uncertainty 10 times smaller than the other measurements is strongly weighted.
The 1989 IUPAC (1991) "best measurement from a single natural source" for isotopic abundances of U are : 238U= 99.2745 ±10, 235U= 0.7200 ±1 (1s?) after Cowan & Adler (1976, GCA, 40).

Comment on the values by Jaffey et al.
............The recommended half-lives for 238U and 235U are more or less from the same source and are thus about similar for all experts. The measurements done by Jaffey et al. for the half lives of U-235 and U-238 are reported with optimistic margins of 0,07% and 0,05% respectively on the activity alone. This low uncertainty concerns the statistic uncertainties. The additional systematic uncertainties have not been estimated by the authors who believe that they do not exceed twice the statistical uncertainties. For comparison, a recent paper on the activity of 237Np (also alpha emission and a long half-life) shows uncertainty bars at 0.3 %. Maximum uncertainty three times as originally given could thus be considered for the U isotopes (for example T1/2 238U= 4.468 ±7 Ga). The obtained order of magnitude for the uncertainty would remains the smallest among the geochronologically useful unstable isotopes.

232Th

-"Physicists' value"
The data in ENSDF are as follows:
............232Th......L 0......0+............1.405e+10 y 6............910807
..................130 e+8 y (10Ge01),..........PHMAA 20 691
..................139 e+8 y 3 (38Ko01)*,......PHRVA 54 413
..................145 e+8 y 5 (56Ma43)*,......JNCEA 2 243
..................139 e+8 y 3 (56Pi42)*,........NUCIA 4 1525
..................142 e+8 y 7 (56Se17)*,........PHRVA 104 1629
..................141 e+8 y 1 (60Fa07)*,........CJPHA 38 1059
..................140.1e+8 y 7 (63Le21)*,.......Pretoria (Nucl En.Appl Isot Rad) Proc, p. 83, LeRoux

- Geochronologists' value
The preferred value is the most recently published by Le Roux & Glendenin (1963: 14.01± 0.07 Ga)

- Chemists' value
Holden (1990) reports the 6 values quoted above in ENSDF (starred ref. above) and calculates a weighted average which is recommended as 14.0 ±0.1 Ga.

147Sm

The 147Sm simply decays by a emission to 143Nd, Ea = 2310 keV.
- "Physicists' value"
The data in ENSDF are as follows:
............147Sm......L 0.0......7/2-............1.06e+11 y 2............920827
T from 147Sm A decay (70Gu14), JINCA 32 3425

............Others: 1.08e+11 y 2......(65Va16)......AAFPA VI 177
.........................1.05e+11 y 2......(61Wr02),....PHRVA 123 205
.........................1.04e+11 y 3......(64Do01),....NUPHA 50 489

- "Geochronologists' value"
The half-life for 147Sm is discussed by Gale (1982) and is deduced from the same set of experimental data compared to Nubase/ENSDF. Three values were obtained by liquid scintillation at 105 ±2 (Wright et al., 61), 104 ±3 (Donhofer, 64), 108 ±2 (Valli et al., 65) and one by using a cylindrical ionisation chamber 106 ±2 Ga. The four values are consistent and the calculation of a weighted mean seems justified resulting in a value of 106.0 ±0.8 (1s) Ga. In contrast, the compiler for ENSDF did not weighted the data and preferred a pessimistic uncertainty estimate of ±2 Ga which agrees with all central values and seems to derive from the single work by Gupta & MacFarlane, 1970. It seems that the weighted mean can be preferred.

- "Chemists' value"
The recommended half-life (106 ±2, Holden, 1990) is the weighted average of Beard & Kelly, 1958 (106 ±4 Ga), Gupta & MacFarlane, 1970 (106 ±2), Al Bataina & Janaeke, 1987 (105 ±4). The most recent measurement published in 1987 is only quoted in the chemist's recommendation; however, the uncertainty bar makes this result poorly constraining the half-life value.
The 1989 IUPAC (1991) "best measurement from a single natural source" for isotopic abundances of Nd are: 142Nd= 27.16 ±4, 143Nd= 12.18 ±2, 144Nd= 23.83 ±4, 145Nd= 8.30 ±2, 146Nd= 17.17 ±3, 148Nd= 5.74 ±1, 150Nd= 5.62 ±1 (2s) at.% after Holliger & Devillers et al. (1981, EPSL, 52).
The 1989 IUPAC (1991) "best measurement from a single natural source" for isotopic abundances of Sm are: 144Sm= 3.076 ±1, 147Sm= 14.995 ±1, 148Sm= 11.242 ±1, 149Sm= 13.819 ±1, 150Sm= 7.380 ±1, 152Sm= 26.738 ±2, 154Sm= 22.750 ±1 (2s) at.% after Lugmair et al. (1975, GCA, 6).

- Comment (147Sm):
The information used by both physicists and geochronologists is the same. The weighted average of 70Gu14=106(2), 65Va16=108(2), 64Do01=104(3), and 61Wr02=105(2) yields 106.0 Ga ±1.1 (1sd) with a normalised chi of 0.75. The other 2 references quoted by Holden (58Ke and 87 Al) give results which are consistent with this weighted average. New activity measurements could be planned for improvement of the precision.

87Rb

-"Physicists' value"
The data in ENSDF are as follows:
............87Rb......L 0.0......3/2-............4.75e+10 y 4
............weighted average of 4.72 4 (66Mc12) and 4.88 8 (74Ne14);

............Others : 5.25 10 (61Mc07), 4.72 8 (60Ra01), 4.7 1 (59Fl40), 4.77 10 (64Ko11), 5.21 15 (65Br25), 5.3 3 (52Le24), 5.82 10 (61Eg01), 5.53 10 (61Be41), 5.53 10 (61Be41), and 5.80 12 (62Le08), all numbers are in units of 1e+10 y.

The evaluator adopted only the most recent measurements of 66Mc12 (47.2 ±0.4 Ga), who determined the amount of 87Sr produced in 87Rb ß- decay, and of 74Ne14 (Neumann & Huster, 1974, absolute counting in proportional counter), where systematic errors which were shown to be inherent to the previous measurements (see 76Ne10) were avoided to a large extent.

Comment:
The physicists' half-life of 47.5 ±0.4 Ga (ENSDF) is the weighted mean of 48.8 ±0.8 Ga (N & H, 74) and of the previous measurement at 47.2 ±0.4 -1s- Ga (by McMullen et al., 66). Because the latter was published more precise than the former, it is weighted more heavily in the weighted mean preferred by the compiler of ENSDF. This leads to several remarks:
- There are no new direct experimental data published on the decay of 87Rb since 1977 and the difference between the geochronological and the physical recommendation is due to differing treatments of the same data;
- The 2 results at 47.2 ±0.4 Ga and 48.8 ±0.8 Ga are inconsistent at 1 sd and consistent at 2 sd. The use of a weighted mean can be questioned;
- The 1966 value is given with a 1 % uncertainty margin, but the 1976 value is favourably commented in ENSDF as taking into account more carefully the experimental errors. Thus the 48.8 value should have been weighted more heavily instead of the reverse.

- "Geochronologists' value"
The geochronological half-life for 87Rb derives mostly from Neumann & Heuster 74; 76 (proportional counting, 48.8 ±0.8 -1s- Ga). This value is not precise enough. However, it was preferred (SJ 77) also for two reasons: 1- in 1977 it appeared that this work gave the best founded measurements and 2- oral presentations during the SOG meeting in Sydney showed that intercomparisons between K-Ar and Rb-Sr ages would better agree using 48.8 than using a lower value including 47.2 which is more than 3 % smaller. In short, the value recommended by the physicists does not appear as superiorly founded versus the geochronological value for the half-life of 87Rb.

- "Chemists' value"
Holden (1990) recommends the unweighed mean of 48.8 ±0.8 by Neumann & Huster, 1974 and of Davis et al., (1977) = 48.9 ±0.4; the latter is said to be the McMullen et al's 1966 revised value.
The 1989 IUPAC (1991) "best measurement from a single natural source" for isotopic abundances of Rb are: 85Rb= 72. 1654 ±132, 87Rb= 27.8346 ±132 (2s) at% after Catanzaro, Murphy et al. (1969. J. Res. NBS, 73A). The 1989 IUPAC (1991) "best measurements from a single natural source" for isotopic abundances of Sr are: 84Sr = 0.5574 ±16, 86Sr= 9.8566 ±34, 87Sr= 7.0015 ±26, 88Sr= 82.5845 ±66 (2s) at.% after Moore, Murphy et al. (1982. J. Res NBS, 87)

General comment (87Rb) :
The reference Davis et al. (1977) is not quoted by physicists but quoted (in press) by geochronologists. Davis et al. have quantitatively measured the decay of Rb in samples from 3 batches coming from a Sr-free sample of, originally 1 kg heavy, RbCl formerly prepared in 1956 by McMullen et al.. McMullen et al. measured the amount of radiogenic accumulated after 7 years. Davis et al. comment that McMullen et al. "did not monitor mass fractionation during measurements" and they remeasured the Sr content 19 years after crystallisation. Calculation were done assuming a value for 86Sr/88Sr ratio at 0.1194 for mass fractionation problems. The overall mean decay obtained for the independent analyses of the different batches is 1.419 ±0.012 10-11/a corresponding to a half-life of 48.9 ±0.4 Ga according to Davis et al. 1977 (48.85 ±0.41 Ga). The unweighed mean preferred by Holden (48.8 ±0.5 Ga) appears well founded.
In addition to direct activity measurements and accumulation of daughter isotope, an estimate of the 87Rb decay has been proposed by Minster et al. (1982). These authors admit that the Rb-Sr age of meteorites (H- E- and LL-chondrites) should reflect the initial age of the solar system which is precisely accepted by them (from U-Pb ages) at 4.555 ±0.010 Ga. They measure the Rb and Sr isotopic compositions of many meteorites assumed to be of this age and conclude that, for these compositions to be obtained today, the decay of 87Rb to 87 Sr should be with a half-life of 49.44 ±0.28 Ga. No new investigation seems to have been undertaken on this problem in the mean time (J.-F. Minster, pers. comm. I-99). The estimate at 49.4 is consistent with the geochronological recommended value and is probably the most recent (indirect) estimate for the 87Rb decay. It could be added to the ENSDF with the following restriction (Manhès, pers. comm. I-99) the actual age of meteorites is "model dependent" and the half-life at 49.4 must be considered a maximum (possible) value (see next report with Manhès).
Recent analytical techniques seem to be able to improve the situation and additional measurements could be planned in a near future.

40K

Decay scheme of the 40K isotope

The total half life of 40K (Tt) is the addition of four components (see Gale, in Odin, 1982 Numerical Dating in Stratigraphy, Réf. n° 100) as shown in the figure (clic decay 40K.jpg).

............-e capture through 1.46 MeV...........-> 40Ar........................(counting rays)
............-e capture direct to ground state...........-> 40Ar........................(inferred from theory versus ß+)
............-positron emission...............................-> 40Ar........................(inferred from ß+/ß- ratio)
............-negatron emission..............................-> 40Ca........................(direct ß- counting)

- "Physicists' value"
............40K.......L 0.........4-........................Tt: 1.277e+9 y 8............941006
............from 73Enva. NUPAB A214
The corresponding physical data displayed in Nubase are: half life = 1.277 ±0.008 Ga, ß-/EC branching r = 0.0117 ±1 (at.%).

Comment : The reference Endt, 1990 is quoted as the most recent one for data on 40K; in fact it fully derives from 73Enva. (Endt & Van der Leun, 1973, Nuclear Physic A214) which itself derives from 67EN (Nuclear Physic A105). The atomic ratio is given at 0.0117 ±1 in Nubase/Nuclear data sheets; this seems to be a rounded value; the use of such imprecise rounded value would make any K-Ar dating by any technique uncertain by about 0.9 % for this factor alone; this rounded number is not appropriate for geochronological application. The calculation of the recommended half life depends on the 40K abundance which, in the original work 73Enva, is accepted at 0.01178 (±4) at.%; the latter value is in contrast to the acceptedly better value by Garner et al., 1975 (see below).

- "Geochronologists' value"
The physical information useful for calculating a K-Ar age needs to consider both the total half-life for 40K and the branching ratio between the ß decay and the e-capture decay.
The geochronological age calculations are based on Beckinsale & Gale (1969) and Garner et al. (1975). Beckinsale & Gale evaluated the literature and selected 5 reliable determinations (NB1) for ß activity and 4 for activity (NB2), they calculated a weighted mean activity which, combined to an atomic abundance of 40K= 0.0118 at.% lead to a half life of 1.265 Ga and a branching ratio ß/e of 89.52 / 10.48 %.
However, using an atomic weight for K at 39.098304 ±0.000058 and a more reliable (Garner et al., 1975) 40K atomic abundance of 0.01167 ±0.0004 % a recalculated half-life of 1.250 Ga (±0.002) is preferred (see detail in Gale, 1982).

Comment : According to our knowledge on the usual errors on ß- and activities (and on the accuracy of the 40K abundance which is not considered), the uncertainty bar of ±0.002 on the total half life accepted by Gale seems to be optimistic. NB 1- data selected by Gale are from: Egelkraut & Leutz, 1960 (1966?); Saha & Gupta (1960); Glendenin, (1961); Brinkman, Aten & Veenbour (1965); Leutz, Schulz & Wenninger (1965). NB 2- data selected by Gale are from: Egelkraut & Leutz, 1960 (1966?); Saha & Gupta (1960); Leutz, Schulz & Wenninger (1965); de Ruyter, Aten et al., (1966).

- "Chemists' value":
Total half-life of 40K is given at 1.26 ±0.01 Ga by Holden (1990). This corresponds to the addition of the 2 separately averaged ß- and EC decay branchs (Holden, 1990, recommends unweighed averages). Recently, R. Helmer reevaluated the decay constants using the data compiled by Endt & Van der Leun (1973), the 40K abundance at 0,0117 (1) % (recommended by IUPAC), and concluded to a total half-life of 1.265 ±0.013 Ga (personal communication to MMB).
The 1989 IUPAC (1991) "best measurements from a single natural source" for isotopic abundances of K are: 39K = 93.25811 ±292; 40K= 0.011672 ±41; 41K= 6.73022 ±292 (2s) at.% (from Garner, Murphy et al., 1975)
and for argon: 40Ar= 99.6003 ±6, 38Ar= 0.0632 ±1, 36Ar= 0.3365 ±6 at.% after Nier (1950).

Table: Source of counting experiments selected by Holden (1990) for calculation of the corresponding half lives (given in Ga).
Starred values are the ones previously used by Endt & Van der Leun (1973) (physicist's value); 6 additional values for EC and one additional value for ß- were used by Endt & Van der Leun (1973) but were considered unreliable by Holden 90. Bolded values are those selected by Beckinsale & Gale (for the value accepted by geochronologists).

____________________________________________________________________________
............................................................ß-...................................................................EC
Good (1951)......................................1.46 ±0.03*.....Wetherill (1957)....................11.7 ±0.4*
Kono, (1955).....................................1.36 ±0.05........De Ruytter, Aten et al.(1966).12.2 ±0.2
McNair (1956)...................................1.44 ±0.01*.....Cesana & Terrani (1977).......12.3 ±0.04
Kelly et al. (1959)..............................1.46 ±0.03*
Saha & Gupta (1960).........................1.37 ±0.04*...................................................12.3 ±0.6*
Glendenin (1961)...............................1.40 ±0.015*
Fleishman & Glazunov (1962)...........1.45 ±0.4 (±!)*
Brinkman et al. (1965)........................1.36 ±0.02*
Leutz, Schulz & Wenninger (1965)....1.40 ±0.002* (±!).........................................12.2 ±0.3*
Feuerhake & Hinzpeter (1966)...........1.41 ±0.02*
Egelkraut & Leutz (1966)...................1.40 ±0.07.....................................................11.8 ±0.5
____________________________________________________________________________


Comment : Concerning the half-life at 1.26 recommended by Holden, such imprecisely calculated value cannot be used in geochronology. Compared to the estimates used by physicists (all measurements are previous to 1966) and geochronologists, the single new data in Holden (1990) is the one by Cesana & Terrani (1977) which published the most precise value at 12.3 ±0.04 for the EC half life. According to Beckinsale & Gale, the data by Leutz et al (1966) and De Ruytter et al. (1966) are demonstrably of better quality and must be weighted more heavily. The most important branch is the ß- decay; B & G do not use a number of high ß- values (1.41, 1.45, 1.45, 1.44, and 1.46) which are either not known (1.41: Feuerhake & Hinzpeter) or considered of poorer reliability, and Holden does not weight the values in contrast to B. & G. The new, more precise value of Cesana & Terrani is also on the higher side compared to previous and less precise data.
This explains the difference in the recommended total half life value. A total half life value slightly higher than the one presently accepted by geochronologists (1.250 Ga) seems to be probable.

3. Data for recently considered geochronological systems

No conventional values were recommended by the SOG for the decay of 187Re and 176Lu. These two isotopes are however used by geochronologists.

187Re

-"Physicists' value"
Data in ENSDF are as follows:
..............187Re.......L .......0.0........5/2+............4.35e+10 y ±13............910220
from 86Li11. NATUA 320 246 measured growth of 187Os daughter.

..............Other values: 3.5e+10 y 4.......(84Na04),
....................................4.56e+10 y 12...(83lu09,80lu10),
....................................6.6e+10 y 13.....(65Br12),
....................................4.3e+10 y 5.......(63Hi08),
....................................3.e+10 y............(62Wa15) from specific activity measurements.
....................................6.2e+10 y 7.......(58He06), from measurements of daughter growth;

Specific activity measurements are expected to yield systematically higher values because of unobserved decay to bound states in the daughter.
...............Other references: 48Na01, 48Su01, 54Su45, 54Hi35, 54He79, 54Di18, 55Di16, 57Wazz, 57Wozz, and 58Na08.

- "Geochronologists' value":
Renne et al., 1998 refer to Lindner et al. (1989) for the ß- decay of 187 Re. Lindner et al. determined the half life to be 42.3 ±1.3 (2s) Ga using chemical methods and mass spectrometry for measuring the daughter 187Os isotope. This information which probably supersedes the physicists' recommended value still remains to be included in Nubase.
Luck & Allègre (1983), considered the fact that Re and Os are siderophile elements so that they are present in iron minerals of the geological objects including meteorites. Luck & Allègre measured Re and Os isotopes by isotope dilution in a mass spectrometer; iron chondrites and the iron phase of other chondrites for which the authors assume a geological age of 4.550 Ga (the U-Pb geochronological age) were investigated. They observed no significant age difference between iron chondrite and the iron phase of other meteorites which plot on a single line on an isochron diagram. A half-life of 45.6 ±1.2 Ga can be calculated for the 187Re using the assumed age of 4.555 Ga for the closure time of the Re/Os system in meteorite. Other authors suspect that iron chondrite may have been closed at an age younger than other meteorites and the solar system and thus the half-life value of 45.6 Ga should be considered a maximum one in agreement with the most recent ideas (G. Manhès, pers. communication. I-99).

- "Chemists' value"
The recommended half-life of 42 ±2 Ga is said to come from the unweighed average from 4 values: 43 ±5 (Hirt et al., 1962), 45 ±2 (Luck & Allègre, 1983; in fact 45.6 ±1.2), 35 ±4 (Naldrett, 1984) and 42.3 ±1.3 (Lindner et al., 1989). The actual arithmetic average is 41.5 Ga.

The 1989 IUPAC (1991) "best measurements from a single natural source" for isotopic abundances of Re are: 185Re= 37.398 ±16, 187Re= 62.602 ±16 (2s) at. % after Gramlich, Murphy. et al. (1973, J. Res. NBS, 77A).
The 1989 IUPAC (1991) "best measurements from a single natural source" for isotopic abundances of Os are: 184Os= 0.018 ±2, 186Os= 1.59 ±5, 187Os= 1.64 ±5, 188Os= 13.27 ±12, 189Os= 16.14 ±14, 190Os= 26.38 ±20, 192Os= 40.96 ±14 ?s at% after Nier (1937, note that this composition could be verified with modern facility).

Comment (187Re) : New activity measurements would be needed to improve the knowledge of that isotope; waiting for this, the last value obtained by Lindner et al. (1989) must be preferred.

176Lu

- "Physicists' value"

.............The data in ENSDF are as follows:
............176Lu....L.....0.0............7-............4.00e+10 y 22............ 980717
............from unweighted average (reduced |h{+2}=6.0) of
............3.6 e+10 y 1............(65Br15), NUPHA 67 417
............5.0 e+10 y 3.............(67Sa05), NUPAB A103 134
............3.79e+10 y 3............(72Ko50), NUPAB A198 73*
............4.08e+10 y 24..........(80No01), PRVCA C21 1109
............3.78e+10 y 2............(83Sa44), RRALA 58 263
............4.05e+10 y 9............(90Ge05), PRVCA 41 2878 and
............3.73e+10 y 5............(92Da03) ARISE 43 69
........................using the Limitation of Relative Statistical Weights method (88WoZO).

The uncertainty in the average value was expanded to include the most precise value of 3.78e+10 y 2 (83Sa44). The input values were measured by g-ray counting with good energy resolution for isotope identification.
The following results may have significant systematic errors because they were measured using ß counting on weak natural Lu2O3 sources, which may have been contaminated with thorium or determined with less reliable methods (90Ge05):
7.3e+10 y 2 (39Li13), 2.15e+10 y 10 (54Ar03), 4.56e+10 y 30 (54Di18), 2.1e+10 y 2 (57Gl84), 2.17e+10 y 35 (58He42), 3.6e+10 y 1 (61Mc12), 2.18e+10 y 6 (64Do01), 3.27e+10 y 5 (69Pr11), 3.57e+10 y 14 (83Pa11), 3.5e+10 y 5 (82Sg01)

The half-life for 176Lu shown in Audi et al. (1997) is 37.8 ±0.2 Ga; it derives from the 1996 evaluation of Nuclear Data Sheets and the above quoted one (40.0 ±2.2 Ga) is the 1998 version.

- Geochronologists' value
The decay of 176 Lu was not considered by the Subcommission n Geochronology (in SJ77). It has been diversely used in geochronological laboratories. The half-life compiled from physical experiments by Faure (1977) is often quoted at 35.4 ±1.1 Ga. Renne et al. 98, consider the result by Tatsumoto et al., 81 (35.7 Ga) as representative.

- "Chemists' value"
The recommended (Holden, 1990) unweighed average half-life at 38 ±1 Ga considers 5 selected results of activity measurements by Komura et al., 1972 (37.9 ±0.3 Ga) Norman, 1980 (40.8 ±2.4), Sguigna et al., 1982 (35.9 ±0.5), Patchett, 1983 (35.7 ±1.4), Sato et al. 1983 (37.8 ±0.2).
The 1989 IUPAC (1991) "best measurements from a single natural source" for isotopic abundances of Lu are: 175Lu= 97.416 ±6, 176Lu= 2.584 ±5 (2s) at.% after Patchett (1983). The 1989 IUPAC (1991) "best measurements from a single natural source" for isotopic abundances of Hf are : 174Hf= 0.1621 ±9, 176Hf= 5.2056 ±17, 177Hf= 18.6060, 178Hf= 27.2969 ±13, 179Hf= 13.6289 ±19, 180Hf= 35.1005 ±22 (2se) at.% after Patchett (1983).

- An additional recent experimental data has been obtained by Nir-el & Levi; they use the same (gamma spectrometry) analytical technique like Gehrke et al. and Dalmasso et al.
............Gehrke et al. (1990, Phys. Rev.)........................40.5 ±0.9 Ga
............Dalmasso et al. (1992, Appl. Rad. Isot.)............37.3 ±0.5 Ga
............Nir-el & Levi (1998, Appl. Rad. Isot.)...............36.9 ±0.2 Ga

The latter authors recommend to consider the weighted mean of 3 preferred data sets by Sato et al., 1983 (37.8, ±2 1sd), Dalmasso et al (37.3 ±0.5 Ga) and their own result at 36.9 ±0.2 Ga. These are the last 3 data published in the literature except for Gehrke et al. (1990) that they reject because the Lu activity was measured from a powder (solid) form sample and this may have led to gamma-ray self-attenuation; Nir-el & Levi (1998) thus suggest a combined value at 37.3 ± 0.1 Ga.

General comment (176Lu) :
The report by Holden (1990) does not consider the 3 most recent papers published about the Lu decay. Among the 5 data selected by Holden, those by Sguigna et al. (1982) and Patchett (1983) are considered to be of low reliability by the evaluator in ENSDF. The high value by Gehrke et al. (1990) is considered suspect both by physicists (in ENSDF) and in the paper by Nier-el & Levi.
From quick reading of the last 3 published papers, nothing can obviously explain the high value by Gehrke et al. compared to the low values by Dalmasso et al. and by Nir-el & Levi. The three studies similarly deduce the gamma activity. In our opinion, the uncertainty margin given by Nir-el & Levi (about 0.5 % of the half-life) seems to be underestimated as well as the one by Dalmasso et al. whose paper gives little experimental information in contrast to the paper by Gehrke et al.
Il semble y avoir deux groupes de valeurs: entre 36 et 38 d'un côté et entre 40 et 41 de l'autre. L'intervalle "physique" de 40,0 ±2,2 Ga paraît criticable car:
-d'un coté aucune donnée publiée ne semble nécessiter une valeur maximale de 42,2 Ga tandis que
-de l'autre, de nombreuses valeurs "mesurées" sont exclues par le minimum de 37,8 Ga. Le vrai intervalle de variation des valeurs semble être au maximum entre 35.7 et 40.5 et, en gros, entre 36 et 40 (ou 38 ±2 Ga) plus ou moins comme le propose Holden 90 mais la distribution des valeurs mesurées se concentre aux deux extrêmes de l'intervalle ce qui suggère qu'un des groupe de valeurs est erroné et qu'il ne faut pas faire une moyenne de ces résultats. Des informations analytiques supplémentaires pourraient seules résoudre le problème avec sécurité.
The value suggested by Renne et al. after Tatsumoto et al. seems to be low; a higher value such as the one at 37.3 Ga (Nir-El & Levi) would be more appropriate.

4. Major problems and possible solutions

From this review, it appears clearly that the major problem for improvement of the precision of the decay constants used in geochronology is the apparent lack of interest for the determination of these constants during the last 20 years. There are probably 2 main reasons which are :
............i- the feeling that the decay constants and other values such as isotopic composition of the elements is well-known and agreed and
............ii- the difficulty to obtain relevant data.
Concerning the former point, it must be pointed out that all but the U decay constants are insufficiently known as far as accuracy is concerned. The precision given in the 20 years old literature is often overestimated and modern data would probably not considerably improve the precision but could most probably lead to more accurate values.
Concerning the latter point, the major problem seems to be the availability of appropriate sources to be measured using modern facilities.
Projects for improvement of the situation will need a cooperation between several groups of scientists including physicists, chemists and geochronologists. This question is addressed now by the people who contributed the present reports in this volume and the Subcommission will encourage this research and search for support.

Summary table. A comparison of the half-lives and other constants recommended by the 3 communities.
__________________________________________________________________
............Geochronologists.....................Physicists (ENSDF)........Chemists
__________________________________________________________________
T1/2 238U= 4.4683 ±24 Ga (1)...........4.468 ±0.003Ga..............4.47 ±0.02 (14)
235/238= 137.88 (2a).......................... -.......................................= 137.88 (2b)
T1/2 235U= 0.70381 ±48 Ga (1).........0.7038 Ga± 0.0005.........0.704 ±0.1 (14)
T 1/2 232 Th= 14.01 Ga (3).................14.05 Ga ± 0.06..............14.0 ±0.1 (14)
__________________________________________________________________
T 1/2 87Rb = 48.8 Ga (4).....................47.5 Ga ±0.4...................48.8 ±0.5 Ga (15)
85/87Rb = 2.59265 (5).........................-.......................................= 2.59265 (5)
86/88Sr = 0.1194 (6)............................-.......................................= 0.1194 (6b)
84/86Sr = 0.056584 (6)........................-.......................................= 0.056551 (6b)
__________________________________________________________________
T 1/2 40K = 1.250 Ga (8)....................1.277±0.008 Ga..............1.26 ±0.1 (15)
branch. ratio ß/e= 89.52 /10.48 %(8)....ß/e = 89.33 / 10.67 %
40K =0.01167 at. % (9)........................= 0.0117 ±1 at. %...........= 0.011672 ±41 (2s)
40/36at. atm = 295.5 (10).....................-.......................................= 296.0 ±0.6 (10)
__________________________________________________________________
T1/2 147Sm : 106.0 ±0.8(1sd) Ga (7)..= 106 ±2 Ga (7).............106 ±2 (15)
150/149Sm : 0.53406 (11)....................-.......................................= 0.53405 (11)
148/144Nd : 0.241572 (11)..................-.......................................= 0.24087 (11)
__________________________________________________________________
T1/2 176Lu = {35.7 Ga (12)} (poor)....= 37.8 ±0.2 Ga (precise)....38 ±1 (15)
.............................................................40.0 ±2.2 Ga (mean)
NB recent measurements would suggest a value at about 37.3 ± 0.1 Ga.
__________________________________________________________________
T1/2 187Re {42.3 ±1.3 Ga (2sd) (13)} = 43.5 ±1.3 Ga...............42 ±2 Ga (15)
__________________________________________________________________
(1) Jaffey et al., 1971
(2a) Shields, 1960 unpubl.; (2b) Cowan & Adler (1976, GCA, 40) in IUPAC 89 report.
(3) Le Roux & Glendenin, 1963
(4) Neumann & Huster, 1974; Davis et al.; + geological comparisons
(5) Catanzaro et al., 1969
(6) Nier, 1938; Moore et al. 1977; (6b) Moore et al. (1982, J. Res. NBS, 87) in IUPAC 89 report.
(7) same 4 sources cf. Lugmair & Marti, 78 / Gale in Odin 82 / Audi et al., 1997
(8) Beck & Ga., 1969
(9) Garner et al., 1976
(10) Nier 1950
(11) Lugmair & Marti, (1978, GCA Suppl., 6: 1419).
(12) Tatsumoto et al., 1981 (in Renne et al. 98)
(13) Lindner et al., 1989 (in Renne et al. 98)
(14) N.E. Holden, (1989 Pure & Applied Chem., 61: 1483)
(15) N.E. Holden, (1990 Pure & Applied Chem., 62: 941)

5. Conclusion

The progress in the knowledge of the physical constants used in geochronology during the last 20 years can be summarized as follows:

238U & 235U : There is no new measurement available since the 1977 proposal by the subcommission on geochronology (SOG). All 3 communities refer to the original measurements by Jaffey et al. (1971); the values of these authors would appropriately be supplemented with realistic total uncertainties of 0.15 %.

232 Th : All 3 communities refer to approximately the same decay which was published in 1963.

87Rb : The shorter half-life recommended by physicists (47.5 Ga) compared to the value used by geochronologists or chemists (48.8 Ga) is not superiorly founded. Since the 1977 SOG recommendations, only 1 new study has been published by Davies et al. (1977) and their (more precise) result is consistent with the value recommended by the subcommission on geochronology.

40K : Different values are used by the three communities. The longest total half-life used by physicists (1.277 Ga) is based on another (less selective) treatment of the same published data (all were published in 1967 or before) and thus, this half-life cannot be considered as superiorly founded compared to the geochrological one (1.250 Ga). The same is true for the values accepted by the chemists (1.26 Ga), entirely based on data published in 1966 or before with the exception of one (partial) activity measurement published in 1977 which is not distinctly different from previous data. A careful reappraisal of the data selected could possibly lead to increase the total half-life of geochronologists but a really significant improvement of the situation would need new measurements to be undertaken.

147Sm : Taking into account the proposal by Gale (in Odin, 1982) for geochronology, the same published sources (1978 or older) are used by all 3 communities to derive the half-life of Sm at about 106 Ga. The accepted central value is similar for all 3 communities but a different statistic treatment leads the geochronological value to appear more precise.

187Re : No "geochronological" recommendation has been published for this isotope up to now. The values accepted by the physicists and chemists significantly differ because different data are used among the published ones. The most recently published information by Lindner et al. (1989: T1/2 = 42.3 Ga) seems to be the most reliable and was selected by Renne et al. (1998). This value can be recommended; additional modern measurement would be useful for a better security if one considers the widely different values published in the literature.

176Lu : No "geochronological" recommendation has been published for this isotope up to now. Extremely different data are published in the literature which led the physicists to recommend significantly different values in successive reports. Renne et al. (1998) selected a half-life value which appears clearly on the low side of the distribution of the published data (35.7 Ga). Presently, the published data are inconsistently grouped around two distinct values at about 37 Ga and at about 40 Ga and the former seems more often reproduced than the latter.

In short, the data used in 1977 to derive the decay constants recommended by the SOG have not been significantly improved during the last 20 years. This conclusion may appear in contrast to what could have been supposed from recently published papers or reports which complained on the urgent need to revise the decay constants recommended for age calculation. On the contrary, it must be pointed out that a really good selection of the data was realised in 1977 and is still valid.

However, this situation is strongly linked to the absence or very small amount of new measurements during the last 20 years; such fundamental measurements must be encouraged in a near future; this would lead to a much better improvement than recalculations of old measurements for which actual non statistical uncertainties are commonly difficult to evaluate.